A spokesman for the North Korean foreign ministry told the state-run Korea Central News Agency, "It is illogical that the DPRK's nuclear weapons pose a threat to the UK.

"It is a pity that the UK makes an excuse for the building of [nuclear submarines] by finding fault with the DPRK, thousands [of] kilometres away from it."

Watch | North Korea announces 'successful' nuclear test on state TV

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North Korea's comments - which are extremely mild in comparison with some of the threats that it regularly fires off in the directions of Seoul and Washington - come after the new British prime minister led the debate in Parliament over the future of the UK's nuclear submarine force.

Mrs May insisted that the threats to the UK from countries such as Russia and North Korea "remain very real," while there will be more potential dangers in the future.

"We must continually convince any potential aggresors that the benefits of an attack on Britain are far outweighed by their consequences and we cannot afford to relax our guard or rule out further shifts which would put our country in grave danger," she said. North Korea dismissed that claim.

The statement added that while Britain committed troops to the UN forces that took part in the Korean War, from 1950 to 1953, Pyongyang "does not regard it as an enemy as they established diplomatic relations based on mutual respect and equality."

On the same day that Mrs May delivered her speech in Parliament, the North Korean premier, Pak Pong-ju, sent a congratulatory letter on her appointment as prime minister. He expressed hope that May would be successful in developing the country and that relations between London and Pyongyang would "grow strong in mutual interests."